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Robust dynamic input reconstruction for delay systems. (English) Zbl 0963.93043

The paper deals with the system \[ \begin{aligned} \dot x_1 &=A_1x_1+ CDx_2+ f_1(t),\\ \dot x_2 &=A_2x_2+ f(t, x_1,Dx_2)+ B(t, x_1)u(t),\end{aligned} \]
\[ 0\leq t\leq \vartheta,\quad x_1(0)\in X_1,\quad x_2(0)\in X_2, \] a pair of evolutionary equations in Hilbert spaces \(X_1\), \(X_2\) with appropriate definitions of the operators and semigroup generators.
The following “inverse” problem is considered: given the “observation” results \(\xi_i\in X_1\), \(i= 1,\dots, m\), find \(u: [0,\vartheta]\to U\) such that \(|x_1(i\delta)- \xi_i|< h\), \(0< h< 1\) where \(x_1(t)\) is the corresponding solution with the given initial condition and \(i\delta\) are the points of a division of the interval \([0,\vartheta]\).

MSC:

93C23 Control/observation systems governed by functional-differential equations
93C25 Control/observation systems in abstract spaces
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